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- W3097045212 abstract "A special sorting operation called Context Directed Swap, and denoted textbf{cds}, performs certain types of block interchanges on permutations. When a permutation is sortable by textbf{cds}, then textbf{cds} sorts it using the fewest possible block interchanges of any kind. This work introduces a classification of permutations based on their number of textbf{cds}-eligible contexts. In prior work an object called the strategic pile of a permutation was discovered and shown to provide an efficient measure of the non-textbf{cds}-sortability of a permutation. Focusing on the classification of permutations with maximal strategic pile, a complete characterization is given when the number of textbf{cds}-eligible contexts is close to maximal as well as when the number of eligible contexts is minimal. A group action that preserves the number of textbf{cds}-eligible contexts of a permutation provides, via the orbit-stabilizer theorem, enumerative results regarding the number of permutations with maximal strategic pile and a given number of textbf{cds}-eligible contexts. Prior work introduced a natural two-person game on permutations that are not textbf{cds}-sortable. The decision problem of which player has a winning strategy in a particular instance of the game appears to be of high computational complexity. Extending prior results, this work presents new conditions for player ONE to have a winning strategy in this combinatorial game." @default.
- W3097045212 created "2020-11-09" @default.
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- W3097045212 date "2020-11-02" @default.
- W3097045212 modified "2023-09-27" @default.
- W3097045212 title "Classifying Permutations under Context-Directed Swaps and the textbf{cds} game" @default.
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